QGP and Confinement XQCD 2010 Wilhelm and Else Heraeus Seminar Bad Honnef, June X-QCD Japan (S.Motoki, K.Nagata, Y.Nakagawa, A. Nakamura and T.Saito) and V.I.Zakharov Poster Next Talk

I am very proud that Most of the Results here are New!

I regret that ? I do not know the Meaning of the most data. Data are preliminary. Let us think together !

Most data are Quench and color SU(2)

Magnetic Degrees of Freedom and the Confinement G.t’Hooft, Nucl.Phys. B190 (1981) 455 H Shiba and T Suzuki. Phys. Lett. B (1994) 461 A. Di Giacomo and G. Paffuti, Phys.Rev.D56,6816 (1997) Kei-ichi Kondo, Phys.Rev.D58, (1998) ….. J. Liao and E. Shuryak, Phys.Rev.Lett.,101, (2008) M.N. Chernodub and V.I. Zakharov, Phys. Rev. Lett.98, (2007) M.N. Chernodub, A. Nakamura and V.I. Zakharov Phys.Rev.D78:074021,2008 M.N. Chernodub and V.I. Zakharov, Phys.Atom.Nucl.72: ,2009 (arXiv: )

N S Who has seen the Mag. Monopole ? Neither I nor you

Spin System

Singular Configuration, or Vortex No Monopole ! But it looks like,,,

Vortices related to the Confinemen are a 2-d Object and we need Surface Operator S.Gukov and E.Witten, hep-th/ E.Wittten, Fortsch. Phys. 55 (2007) 545. A.DiGiacomo and V.I.Zakharov, hep-th/

Wilson Loops for a charge +e+e -e-e R t

Surface Operator

Center Projection Landau gauge or Coulomb Gauge Gauge Rotation. Therefore non-local Del Debbio, Faber, Giedt, Greensite, Olejnik Phys.Rev. D58, 1998,

Plaquette pierced by a Vortex A Vortex pierces the Plaquette. 1-d Object (Charge) Wilson Loop 2-d Object (Vortex Line) Wilson Loop

Vortex Removing Remember that By definition, now All vortices are fading out (by definition).

Surface Operator Operator AOperator B

Size Dependence of Operator A L A <> L

with/without the Vortices After removing Vortices L

Fitting L

Size Dependence of OperatorB L B <> L

with/without the Vortices L B <> L

AA R R L=1 No Vortex Removal

AA With and Without Vortices R R

AA L=1,2,3 R R

BB With and Without Vortices R

Another Possibility (in Future)

Transport Coefficients One of X-QCD Japan projects is to calculate Transport Coefficients at RHIC and LHC temperature regions and to see if they are different. What does “Perfect Fluid” mean ?

Literature (4) Masuda, A.N.,Sakai and Shoji Nucl.Phys. B(Proc.Suppl.)42, (1995),526 A.N., Sakai and Amemiya Nucl.Phys. B(Proc.Suppl.)53, (1997), 432 A.N, Saito and Sakai Nucl.Phys. B(Proc.Suppl.)63, (1998), 424 Sakai, A.N. and Saito Nucl.Phys. A638, (1998), 535c A.N, Sakai Phys.Rev.Lett. 94 (2005) hep-lat/

History U(1) Coulomb and Confinement Phases SU(2) Two Definitions: F=log U F=U-1 SU(3) Improved Action The first calculation of eta/s on the lattice, which is consistento with KSS bound.

c Viscosity by Lattice, 2007 Nakamura and Sakai  : shear viscosity s: Entroypy density

Fluctuations in MC sweeps Standard Action Improved Action

中川君のデータ２

One Talk, One Topics ! This is SU(3) resuts ! Sorry ! Let us come back to SU(2).

Standard Plaq. Action

With Multi-Hit

+ Vortex Removal

Improve Action (Symanzik)

Conclusion QCD is a Quantum Field Theory. QCD has a very special feature, the Confinement. If a singular structure of the quantum field (gluon field) explains the confinement, it is very interesting (at least to me). The surface operators feel Vortex. Transport Coefficients change if we remove the Vortex. We want to understand QGP natures in terms of the Surface operators in future.

In other words, QCD/QGP physics provides an opportunity to see a new quantum field mechanism, the singularities on surfaces.

Many Thanks Frithjof, Krzysztof and Christian for this nice seminar !